A Geometric Approach to Steerable Convolutions

• URL: http://arxiv.org/abs/2510.18813v2
• Date: Fri, 24 Oct 2025 17:42:45 GMT
• Title: A Geometric Approach to Steerable Convolutions
• Authors: Soumyabrata Kundu, Risi Kondor,
• Abstract summary: This work provides a new and more intuitive derivation of steerable convolutional neural networks in $d$ dimensions.<n>We offer an intuitive explanation for the appearance of the Clebsch--Gordan decomposition and spherical harmonic basis functions.
• Score: 5.257591631753942
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In contrast to the somewhat abstract, group theoretical approach adopted by many papers, our work provides a new and more intuitive derivation of steerable convolutional neural networks in $d$ dimensions. This derivation is based on geometric arguments and fundamental principles of pattern matching. We offer an intuitive explanation for the appearance of the Clebsch--Gordan decomposition and spherical harmonic basis functions. Furthermore, we suggest a novel way to construct steerable convolution layers using interpolation kernels that improve upon existing implementation, and offer greater robustness to noisy data.

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